Purpose:
We assess the increase in total retinal blood flow (TRBF) induced by flicker stimulation of the human retina in vivo and investigate the flicker induced hyperemia by means of a vascular flow model of the retinal circulation to study neurovascular coupling (NC).

Methods:
In six healthy subjects, TRBF was measured before and during stimulation with diffuse luminance flicker. Blood flow velocities in retinal vessels were measured via dual-beam bidirectional Doppler Fourier-domain optical coherence tomography (FD-OCT), retinal vessel diameters were assessed based on FD-OCT phase data. This allowed for the calculation of TRBF before and during visual stimulation. Additionally, a mathematical flow model for the retinal vasculature was adapted to study the implications of diameter variations on retinal perfusion. Measured and simulated perfusion was compared to draw conclusions on the diameter variations in different layers of the vascular tree.

Results:
The measured mean baseline flow was 36.4 ± 6.5 μl/min while the mean flow during flicker stimulation was 53.4% ± 8.3 μl/min. The individual increase in TRBF during flicker stimulation ranged between 34% and 66%. The average increase in TRBF over all measured subjects was 47.6% ± 12.6%.

Conclusions:
Dual-beam bidirectional Doppler FD-OCT allowed quantifying NC in the human retina in vivo and may be a promising method for monitoring alterations in NC caused by various pathologies. The comparison of the measured data with the results obtained in the simulated vasculature indicates that the vasodilation induced by NC is more pronounced in smaller vessels.

The ability of the vascular system to adapt its blood flow to neural regions with a higher metabolic demand was described long ago.1 This phenomenon is called neurovascular coupling (NC) and has been experimentally verified in the brain in numerous experiments.2–5 Standard technologies for in vivo assessment of NC in the human brain include functional magnetic resonance imaging (fMRI) and positron emission tomography (PET). In the retina, this phenomenon exists as well, but neither fMRI nor PET offer sufficient resolution to study the retina.6–8

It has been shown that NC can be studied in the human retina by stimulating photoreceptors with stroboscopic light.8–10 Most of the published data rely on the observation of vascular caliber variations to draw conclusions from vessel diameter changes on flow changes.11–14 Typically, the diameter of a vessel is assessed by fundus photographic techniques, which allow for the real time evaluation of retinal vessel diameter. A large number of studies have been performed to assess vessel diameter changes during stimulation with diffuse luminance flicker in healthy subjects under normal conditions9,11 or during oxygen breathing,15 as well as in patients with diabetes,16,17 glaucoma,18,19 or systemic hypertension.19,20 However, the interpretation of the latter experiments is limited by the fact that only data about retinal vessel diameter, but not about volumetric blood flow, are available.

To measure the response of the retinal and optic nerve head (ONH) blood flow to stimulation with diffuse flicker light, laser Doppler techniques have been used,9,21–26 which, however, offer limited reproducibility and clinical applicability. In recent years, optical technologies have emerged that allow measuring retinal perfusion directly based on optical coherence tomography (OCT). In the present study, we used dual-beam bidirectional Doppler Fourier-domain OCT (FD-OCT), which allows for measuring total retinal blood flow (TRBF) in humans.27 This technique seems most suitable to study alterations in TRBF caused by flicker stimulation, since it enables the measurement at different physiologic perfusion conditions and facilitates comparison of these perfusion states.

In the present study, we quantified TRBF in healthy subjects at baseline condition and during stimulation with diffuse luminance flicker. In addition, we presented a model of the retinal vasculature to explain some of the observations that were made during these experiments.

Methods

Measurement of TRBF by Dual-Beam Bidirectional Doppler FD-OCT

The retinal blood flow measurements presented in this manuscript were performed with a dual-beam bidirectional Doppler FD-OCT system coupled to a fundus camera that has been described previously.27,28 The principle of the method is as follows: Two orthogonally polarized beams of a superluminescent diode are focused onto the same spot at the retina. Here, the light of each probing beam is back-reflected by static tissue and moving particles, like red blood cells (RBCs). In the latter case, the frequency of the light is Doppler shifted. These angle-dependent Doppler shifts are recorded for each of the two beams separately. They contain the information necessary to quantify blood flow velocity. To obtain a cross-sectional image, the focus spot then is moved periodically over the retina via an XY-scanning unit.

The Doppler OCT (DOCT) data were acquired as follows: The spectral signal of each of the two probing channels was recorded individually by two identical spectrometers. Onto the resulting spectral data different preprocessing steps, like a rescaling from λ– to k– space, and a numerical dispersion correction were applied. The latter was necessary to compensate for a possibly remaining dispersion mismatch between sample and reference arm. The processed spectra then were Fast Fourier transformed (FFT) to obtain the OCT intensity images for each channel. Furthermore, from the FFT data, the phase shifts induced by moving scatterers were calculated by subtracting the phase values of the FFTs of consecutive A-scans. To this end, each A-scan was multiplied with the complex conjugate of the previous one. This was done for each channel separately resulting in two phase shift values, Φ1 and Φ2, for each depth position. From this, the absolute velocity of the scatterers was obtained by applying Equation 1:

In this equation, ΔΦ is the difference of the two recorded phase shifts Φ1 and Φ2, λ0 = 838.8 nm is the central wavelength of the light source, n = 1.37 is the refractive index of blood29 and β is the angle between the plane spanned by the two scanning beams and the velocity vector, which was extracted from the fundus images that were recorded simultaneously during the DOCT measurements. The angle Δα in Equation 1 is the angle enclosed by the two probing beams at the ocular fundus. This angle was calculated from the beam separation on the corneal surface and each subject's eye length as measured with the commercially available IOL Master (Carl Zeiss Meditec, Oberkochen, Germany).

To obtain the blood flow Q within a vessel, the calculated blood flow velocity was multiplied with the vessel cross-section. To this end, circular vessel cross-sections were assumed and the vessel diameter was extracted from the phase tomograms by measuring the depth of the vessel along the axis of light propagation.30

To calculate TRBF, the blood flow in each vessel entering or exiting the retina via the ONH must be assessed. To accomplish this, a rectangular scanning pattern as shown in Figure 1 was applied.27

This has the advantage of allowing for an individual selection of each scanning position and enabling the operator to avoid vessel bifurcations or sites with a strong vessel curvature within the scanning region, which could corrupt the measurement. Furthermore, it gives the operator the opportunity to refocus the scanning beams for each position to assure a good focal overlap on the vessels under study.

After calculation of Q in each individual vessel, the blood flow values obtained in all arteries and all veins of a subject were summed up, to obtain total arterial blood flow (TABF) and total venous blood flow (TVBF), respectively. Total retinal blood flow was calculated as the mean of TABF and TVBF. Since the retina is an end organ, TABF and TVBF must be equal to fulfill the law of mass conservation. The relative deviation between TABF and TVBF,

is a good indicator of the reliability and quality of a measurement.

Flicker Stimulation of the Retina

The flicker stimulation of the retina was realized via the Dynamic Vessel Analyzer (DVA) system (Imedos AG, Jena, Germany). The Doppler FD-OCT system was custom integrated into the fundus camera of this DVA by means of a dichroic mirror.27 The stimulation system of the DVA uses a diffuse luminance flicker and operates at a frequency of 12.5 Hz. The flicker stimulation is achieved by rectangular cutting of the fundus illumination of the DVA (530–600 nm, illumination intensity ∼1.96E-04 W/cm2).31

Measuring Protocol

The following study protocol was approved by the Ethics Committee of the Medical University of Vienna and followed the guidelines set forth in the Declaration of Helsinki. Informed consent was obtained from all subjects after explanation of the nature and possible consequences of the study.

First, the right eye's pupil of each volunteer was dilated with one drop of tropicamide (5 mg/ml, Mydriaticum Agepha eye drops; AGEPHA GmbH, Vienna, Austria). After a resting period (∼15 minutes), the volunteer was seated in front of the Doppler FD-OCT setup and asked to look onto the internal fixation target. Then, the TRBF measurement was started.

A diagram of the timeline of the measuring protocol is shown in Figure 2. First, a baseline TRBF measurement was done in each subject. After a short resting period of approximately 5 minutes, the stimulation was activated. After 2 minutes of flicker stimulation, a second TRBF measurement was started while the stimulation continued. The delayed start of the DOCT measurement after onset of flicker stimulation ensures that the flicker-induced vasodilation has taken full effect before the start of the TRBF measurement.

For calculation of the central retinal arterial equivalent (CRAE) and the central retinal venous equivalent (CRVE), the revised formulas for summarizing retinal vessel diameters from the report of Knudtson et al.32 were used. Central retinal arterial equivalent velocity, vCRAE, and CRVE velocity, vCRVE , then were calculated by means of the following equations:

where dCRAE and dCRVE are the diameters of the CRAE and CRVE, respectively, and QTABF and QTVBF are TABF and TVBF, respectively.

Vascular Flow Model

To analyze the impact of diameter changes at different depth levels of the vascular tree, the vascular flow model by Takahashi et al.33 was adapted. In brief, they proposed a network for modeling a major branch of the retinal vasculature (arteriole 108 μm → venule 147 μm)33 that represents a symmetric tree (Fig. 3), which is characterized by a diameter exponent of 2.85 for all layers except for the capillary network. The lengths of the individual vessel segments are calculated based on their radii (L[r] = 7.4r1.14). For the viscosity in the individual vessel segments, they used the formula proposed by Haynes.34 The mean blood pressure in the largest arteriole (108 μm) was calculated based on a hydrostatic and frictional factor to 38.9 mm Hg. They analyzed several hemodynamic parameters over the vascular network tree (e.g., blood flow velocity, blood pressure, pressure gradient) under the assumption of a preset inflow rate.

In our study, the model was used to study patterns of vasodilation over the vascular network tree. To this end, some adaptations were applied: Firstly, the network was generated based on the diameter exponents as found in our in vivo measurements (arteries, 3.01; veins, 2.62). Secondly, the formula for calculation of the viscosity proposed by Haynes34 was replaced by the formula proposed by Pries et al.,35 which yields the relative apparent viscosity that was multiplied with the viscosity of blood plasma (1.10 mPa s) to obtain the viscosity of the whole blood. The formula by Haynes only reflects the decrease in viscosity with decreasing vessel diameter (Fahraeus-Lindqvist effect), but does not take the steep increase of the viscosity in vessels with diameters <6 μm with decreasing vessel diameter into account. Therefore, Takahashi et al.33 estimated the viscosity in those narrower vessels based on the ratio of the fourth power of radii. The formula by Pries et al.,35 on the other hand, considers the viscosity characteristics in the entire diameter range of interest down to vessels with diameters <6 μm. Thirdly, the simulated flow values were not calculated based on a preset inflow rate into the system, as done by Takahashi et al.,33 but from the flow resistance of the whole network and the pressure gradient between the largest arteriole and the largest venule (21 mm Hg).33 The flow resistances in individual vessel segments were calculated according to Hagen-Poiseuille's law allowing the determination of the flow resistance of the whole network. From this, the flow in individual vessel segments was calculated by applying the law of mass conservation.

In addition to the baseline system, three scenarios of vasodilation were modeled (see Fig. 4) by adapting the diameters of the individual vessel segments for arteries and veins: For the first scenario, the magnitude of the increase in vessel diameters decreases linearly from one layer to the next, starting in the layer containing the smallest vessels with an increase of 20% to the top layer where an increase of 8% was simulated for the arteries and 9.8% for the veins (vasodilation predominant in smaller vessels). These diameter changes of 8% and 9.8% respectively, were chosen based on our in vivo measurements (see Results section). In the second scenario, the increase of the vessel diameter was linearly distributed from 0% in the layer containing the smallest vessels up to 8% and 9.8% in the layer containing the largest artery and vein, respectively (vasodilation predominant in the larger vessels). Finally, in the third scenario the increase in vessel diameter was linearly accumulated from 8% in the largest artery to 9.8% in the largest vein (vasodilation almost constant over all vessel sizes).

Model of the retinal vasculature represented by a binary tree. The vessels bifurcate in a dichotomous manner except for the precapillaries, which are point of origin of four capillaries. Adapted from Takahashi et al.33

Figure 3

Model of the retinal vasculature represented by a binary tree. The vessels bifurcate in a dichotomous manner except for the precapillaries, which are point of origin of four capillaries. Adapted from Takahashi et al.33

Relative diameter changes applied in the binary tree model to simulate different flow states. For scenario 1, the increase in diameter decreases from 20% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (red). In scenario 2, the increase in diameter accumulated from 0% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (blue). In scenario 3, the increase in diameter accumulated from 8% in the largest artery to 9.8% in the largest vein (green). The x-axis of the plot corresponds to the layer of the vascular tree.

Figure 4

Relative diameter changes applied in the binary tree model to simulate different flow states. For scenario 1, the increase in diameter decreases from 20% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (red). In scenario 2, the increase in diameter accumulated from 0% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (blue). In scenario 3, the increase in diameter accumulated from 8% in the largest artery to 9.8% in the largest vein (green). The x-axis of the plot corresponds to the layer of the vascular tree.

For further analysis of the simulated network's perfusion and of the effects on the latter by vascular changes, the flow values of individual vessel segments in distinct layers were plotted over the vessel segments' corresponding diameter in a log-log plot. The slope of a power fit into these values was analyzed for the three different scenarios of vasodilation and compared with the fits that were obtained in similar plots generated from the in vivo data measured at baseline conditions and during stimulation with diffuse luminance flicker in the subjects.

To analyze the influence of different diameter variations on the pressure distribution over the vascular tree, we calculated the pressure gradients over individual vessel segments according to Hagen-Poiseuille's law. This allowed comparing the absolute pressure distribution and the pressure gradients over the different vessel layers of the vascular tree before and after vasodilation.

Data Analysis

Paired t-tests were performed to compare TRBFs, CREs, and power fit exponents obtained at baseline condition and during stimulation with diffuse luminance flicker. A linear correlation analysis was performed between TRBFs and CREs, between CREs and CRE velocities, and between relative diameter variations assessed by DOCT and DVA. A value of P < 0.05 was considered the level of significance for all calculations. Statistical analysis was performed using SPSS version 22 (SPSS; IBM, Armonk, NY, USA) and MATLAB (Release 2014b; MathWorks, Inc., Natick, MA, USA).

Results

Six healthy volunteers were measured (two female, four male) with an average age of 30.3 ± 9.5 years. Table 1 shows systolic blood pressure (BP), diastolic BP (DBP), intraocular pressure (IOP), pulse rate (PR), mean arterial pressure (MAP), and ocular perfusion pressure (OPP) for each subject and the mean and standard deviation of the obtained parameters over all subjects.

The measured TRBF for each subject at baseline and during flicker stimulation condition is depicted in Figure 5a. The relative deviations between arterial and venous flow are depicted in Table 2. As can be seen, the deviation between inflow and outflow is below or equal to 15% for all except one measurement. The mean baseline flow was 36.4 ± 6.5 μl/min and the mean flow during flicker stimulation was 53.4 ± 8.3 μl/min (t-test, P < 0.001). Figure 5b shows the relative TRBF increase for each subject. The mean increase in TRBF was 47.6% ± 12.6% with individual variations between 34% and 66%.

To verify the correlation between TABF/TVBF and CRAE/CRVE, the values were plotted against each other in Figure 7. It shows that the TABF correlated well with the CRAE at baseline (r = 0.565, P = 0.242) and during flicker stimulation (r = 0.569, P = 0.239). On the other hand, TVBF and CRVE correlated well at baseline (r = 0.454, P = 0.366) but weakly during flickering stimulation (r = 0.144, P = 0.786).

Total arterial blood flow and TVBF over CRAE and CRVE, respectively, at baseline and during flicker stimulation. Central retinal arterial equivalent and TABF correlated well in the subjects at baseline (black) and during flicker stimulation (blue). Central retinal venous equivalent and TVBF correlated well at baseline (red), but weak during the flicker stimulation (pink).

Figure 7

Total arterial blood flow and TVBF over CRAE and CRVE, respectively, at baseline and during flicker stimulation. Central retinal arterial equivalent and TABF correlated well in the subjects at baseline (black) and during flicker stimulation (blue). Central retinal venous equivalent and TVBF correlated well at baseline (red), but weak during the flicker stimulation (pink).

In Figure 8a, the increase of CRAE and vCRAE and in Figure 8b, the increase of CRVE and vCRVE are plotted. In all subjects the relative increase in blood velocities was more pronounced than the relative increase in vessel diameters.

In Figure 9, exemplarily the calculated flow values for all vessels of a single subject (subject 6) are plotted over their respective diameter measurements for baseline condition and during stimulation with diffuse luminance flicker.

Mean Exponents Obtained From Power Fitting Into Flow Over Diameter Values for Different Vessel Types

Table 3

Mean Exponents Obtained From Power Fitting Into Flow Over Diameter Values for Different Vessel Types

The effect of different vasodilation patterns on retinal blood flow rates was studied by means of the binary tree model. The results of the predicted associations between diameter and flow at baseline and during flicker stimulation are shown in Figure 10. The simulated baseline flow resulted to 16.52 μl/min. The increase in blood flow was highest when vasodilation predominately occurred in the smaller vessels (scenario 1: 28.00 μl/min), less pronounced when almost uniform vasodilation was assumed (scenario 3: 23.23 μl/min), and smallest when vasodilation predominately occurred in the larger vessels (scenario 2, 19.23 μl/min).

Flow over diameter in a log-log plot for individual vessels in the four simulated flow states (baseline + three vasodilation scenarios during flicker stimulation) for arteries (a) and veins (b). The respective exponent of the power fit to the data series of each scenario is given in the legends of (a) and (b).

Figure 10

Flow over diameter in a log-log plot for individual vessels in the four simulated flow states (baseline + three vasodilation scenarios during flicker stimulation) for arteries (a) and veins (b). The respective exponent of the power fit to the data series of each scenario is given in the legends of (a) and (b).

Figure 11a shows the effect of the diameter changes on the absolute pressure distribution over the vessel network and Figure 11b depicts the relative changes in the pressure gradients over the individual layers for the three simulated scenarios compared to the baseline system. The pressure decrease is steepest in the larger vessels when vasodilation occurs predominately in the smaller vessels (scenario 1).

(a) Absolute pressure for the simulated vessel segments (mean of the pressures at the inflow and outflow point of each segment) plotted over the corresponding vessel diameters for baseline and all three scenarios. (b) Relative changes of the pressure gradients compared with the baseline system for each layer.

Figure 11

(a) Absolute pressure for the simulated vessel segments (mean of the pressures at the inflow and outflow point of each segment) plotted over the corresponding vessel diameters for baseline and all three scenarios. (b) Relative changes of the pressure gradients compared with the baseline system for each layer.

The present data indicated that flicker stimulation of the retina causes an increase in TRBF. Mean TRBF during flicker stimulation (53.4 ± 8.3 μl/min) was significantly higher in comparison to mean baseline flow (36.4 ± 6.5 μl/min) in all subjects. This represents an increase of almost 50% in TRBF. To the best of our knowledge, only one previous study36 quantified TRBF in response to flicker stimulation. Using a Doppler OCT system relying on double circular scans, the investigators reported a blood flow increase of 22% in 3 healthy subjects, which is considerably less than the changes seen in our study. This can be explained in part by the time delay between flicker stimulation and Doppler OCT measurement. For parts of the retinal vasculature, a variety of previous studies have aimed to measure the change in retinal blood flow during flicker provocation and the results obtained in the present work are closer to what has been reported in this literature. The reported increase in blood flow in individual vessels measured with laser Doppler velocimetry ranges between 43% and 59%,9,26,37 well compatible with the results of the present study. Using adaptive optics scanning laser ophthalmoscopy, Zhong et al.38 reported an increase of retinal blood velocities between 48% and 65% depending on the area of flicker stimulation. This is in reasonable agreement with data obtained using color Doppler imaging that showed a 42% increase in blood velocity in the central retinal artery during flicker stimulation39 as well as data obtained using scanning laser Doppler flowmetry showing an increase in retinal blood flow of 46%.40

The Doppler OCT technology that was used in the present study was validated in a variety of previous studies. These include in vitro experiments,28,41 experiments at retinal vessel bifurcations,41 as well as comparisons versus laser Doppler velocimetry42 and invasive microsphere technology.43 As such, it is interesting that the comparison of DOCT and DVA diameter changes in response to flicker stimulation as presented in the Appendix (Table A1) shows differences for some vessels. In this respect it must be considered that for the presented measurements with the DVA, the vessel diameter was calculated as the mean over at least 20 seconds during baseline and during flicker stimulation. Averaging a continuous measurement over a longer time period smoothens fluctuations in vessel diameter which are caused by vasomotion (see Appendix Figs. A1a and A1b). As can be seen in the FFT in Appendix Fig. A1c, these fluctuations have a frequency of approximately 0.1 Hz, which is in agreement with literature values.44 The fluctuations in diameter due to vasomotion (depicted in Appendix Figs. A1a and A1b) are as high as 6 μm. This must be considered when extracting vessel diameters from DOCT phase data. At an acquisition period of 3 to 6 seconds, some measurements may well be taken at minima or maxima of the vasomotoric cycle. However, this limitation is less severe when TRBF or CRAE and CRVE are assessed, because the effect will average out when many different vessels are measured. This also is reflected in the low relative deviation between TABF and TVBF found in the measurements (see Table 2).

The increase in CRAE and CRVE due to flicker stimulation was in the same range for all subjects. In Figure 7, TABF and TVBF are plotted over CRAE and CRVE for measurements at baseline and during flicker stimulation for all subjects. Central retinal arterial equivalent and TABF correlated well at baseline and during flicker stimulation. At baseline, CRVE and TVBF correlated similarly well. However, the correlation between CRVE and TVBF during flicker stimulation was weak. This as well as the relatively weak correlation between the increase in CRAE and CRAE velocity and the increase in CRVE and CRVE velocity (see Fig. 8) might at first seem counterintuitive. One could expect that an increase in the CRE would lead to a reduced vascular resistance and, therefore, would be associated with an increase in blood flow velocity. However, this only holds true if the main change in vascular resistance is due to diameter changes in the larger retinal arterioles and venules, which were measured with either the DOCT or the DVA system. These values were extracted at sites within one disk diameter distance from the ONH, where the diameters of these vessels typically are between 60 and 170 μm. Consequently, vessel calibers and their changes were extracted at sites that are at a relatively large distance upstream or downstream from the precapillary arterioles and the capillary bed. The latter, however, are known to represent the major site of vascular resistance and, therefore, cause the highest pressure drop in the vascular system.45

With the model of the retinal vascular system, we studied the effect of different patterns of change in vessel diameter on retinal blood flow. The results at baseline (16.52 μl/min) and the scenarios assuming different distributions of vasodilation during flicker stimulation are shown in Figure 10. As expected, the increase in blood flow was highest when vasodilation predominately occurred in the smaller vessels (scenario 1: 28.00 μl/min). Under the assumption of almost uniform vasodilation, the increase in blood flow was less pronounced (scenario 3, 23.23 μl/min). For the scenario where vasodilation predominately occurred in the larger vessels the increase in blood flow was lowest (scenario 2, 19.23 μl/min).

From the previous considerations it becomes clear that a change in vessel diameters measured in larger vessels does not necessarily imply a parallel change in TRBF because it only reflects the local alterations at the measuring sites. This is in good agreement with findings made by Guidoboni et al.,46 who mathematically modeled IOP, BP, and the retinal auto regulation to assess the relationship of those factors. The main determinant of vascular resistance and, as such, of blood flow is, however, the diameter in the microcirculation. This also is confirmed by our simulation, which showed that the amount of blood flow increase strongly depends on the change in vessel diameters along the vascular tree. This also may explain why subjects 1 and 3 have considerably different changes of blood velocity despite their similar level of vasodilation (see Fig. 8). Further exploration of these effects in humans would require measurement of diameters in smaller arterioles and venules as well as capillaries, which may be possible only by adaptive optics technology.47–49

To give an example for the alterations of flow conditions in one subject, the flow was plotted over the diameter in a log-log plot for all vessels of subject 6 at baseline conditions (Fig. 9a) and during stimulation with diffuse luminance flicker (Fig. 9b). In each plot, a power fit was calculated for arteries (red) and veins (blue). It shows that for the measurement during flicker stimulation, both curves were shifted toward higher diameters and higher flow values in comparison with the baseline condition. The mean values of the obtained power fit exponents over all subjects are depicted in Table 3 and lie in the range previously reported in the literature.50–52 The exponents were higher in retinal arteries than in retinal veins and tended to increase during stimulation with diffuse luminance flicker. The increase of the power fit exponents due to flicker stimulation also was analyzed in our modeling (see Fig. 10). The trend of an increase in the exponents as seen in our measurements for arteries and veins was only predicted for scenario 1 in which the diameter increase occurred predominantly in the smallest vessels (see Fig. 10a, legend). However, the amount by which the exponent increased in vivo was higher than in our modeling. In the other two scenarios, the power fit exponents for arteries and veins either stayed constant or decreased. Summing up, these results clearly indicated that in the human retina the diameter increase due to flicker stimulation was more pronounced in smaller vessels than in larger vessels. This also agreed with our recent observation that vasodilation in response to flicker stimulation is the larger the smaller the vessel diameter.53 This also has implications for the pressure within the vasculature and the pressure gradients (as shown in Fig. 11). A dilation of certain vessel segments not only reduces the pressure gradient over those vessels but also redistributes the pressure load to other segments. The comparison between scenarios 1 and 2 showed that dilating the smaller vessels (scenario 1) relieved the pressure gradient over those vessels but induced a higher pressure load on the larger vessels (see Fig. 11b). Vice versa, in scenario 2, where mainly the larger vessels were dilated, an increased pressure load was imposed on the smaller vessels. These effects might have a role in inducing damage to the retinal vasculature in pathologies where NC and vasodilation are selectively impaired in certain layers of the vascular tree while remaining fully functional in others. In contrast to scenario 1, only minor pressure redistributions are seen in scenario 3, in which all vessels are dilated by approximately the same amount. However, according to the considerations concerning the power fit exponents, scenario 3 is unlikely. In conclusion, our modeling suggested in healthy subjects a behavior like in scenario 1 with a more pronounced dilation of the smaller vessels but pressure gradient redistribution within a range ensuring the integrity of the larger vessels.

The intention of the modeling was to get a qualitative overview on the behavior of the power fit exponents and the pressure gradient distributions in a vascular flow network if diameter adaptations are applied to certain layers of the network tree. Yet, when considering the outcome of these simulations, one must be aware of the limitations of the model. First, the vascular system is a much more complex structure than a binary tree. In the retinal vasculature, the branching ratio is not 2 as assumed in the model but varies, depending on the retinal region, between 2.02 and 2.55.54 This fact led to small deviations between measured flow values and simulated flow data: Vessels with a diameter of approximately 108 μm usually show in vivo lower flow values than the 16.52 μl/min yielded from our modeling. During stimulation with diffuse flicker light, it also must be considered that capillary dilation is not uniform over the different retinal capillary layers. Rat experiments indicate that flicker stimulation evokes larger dilations in the intermediate layer capillaries than in the superficial and deep layer capillaries.55 Recently, Duan et al.56 reported a vasodilation of 13% ± 5% in the precapillary arterioles, 31% ± 8% in the capillaries, and 10% ± 3% in the postcapillary venules by using adaptive optics imaging in the human retina while applying focal patches of flickering visible light. For the above reasons, although showing a clear trend, the increases in the power fit exponents as calculated by the model are lower than the ones observed in vivo. These results indicate that regulation of blood flow during neural stimulation is more complex than reflected in our modeling. As such, more complex models57–61 for simulating the vascular system can be used in future to allow more precise predictions of retinal blood flow under different stimuli.

In conclusion, we quantified the increase in TRBF in humans in response to stimulation with diffuse luminance flicker. Our modeling indicated that vasodilation under such circumstances is happening primarily in the microvasculature. Modeling various flow states in a realistic retinal vascular tree model may offer a better understanding of retinal diseases in which the pathogenesis might be linked to reduced perfusion, such as glaucoma, diabetes or neurodegenerative disease of the brain.

To compare the vessel diameters extracted from the phase tomograms with a different measuring modality, in each subject individual vessels were assessed additionally by means of the DVA, into which the Doppler FD-OCT setup was custom integrated. The DVA allows for a continuous recording of the diameter of a retinal vessel with a time resolution of 25 readings/sec. For the DVA measurements, the average of the vessel diameter of at least the last 20 seconds before the onset of the flicker stimulation and of at least the last 20 seconds of the flicker stimulation period were considered baseline and flicker values of the vessel diameter, respectively. Since the DOCT frames used for the diameter measurements were recorded within 3 to 6 seconds while the DVA data were recorded continuously and, thus, allows averaging the vessel diameter over longer periods, a comparison of those techniques allows for studying the time behavior of the vessel diameter. Based on this, the influence of the time span of the recording on the obtained vessel diameter values was examined. Table A1 compares the DVA and DOCT assessment of flicker-induced vessel diameter changes in exemplary individual vessels. While there is some degree of correlation between these measurements, the association is far from being perfect (r = 0.58, P = 0.015).

To study the frequency and amplitude of diameter changes over time, additional DVA measurements in one subject were done over a time span of 10 minutes and analyzed by FFT. Figure A1 depicts the normalized vessel diameter (mean diameter = 157.1 μm) and the corresponding FFT of a 10-minute vessel diameter recording of a major retinal vein, as assessed by the DVA system. In Figure A1a and A1b, sliding averages were calculated for a sliding window of 3 seconds (red, consistent with the DOCT recording time) and 20 seconds (green, consistent with the minimum DVA averaging time used in this study). The FFT depicted in Figure A1c yielded two pronounced peaks, one at the pulse frequency (∼0.73 Hz) and one that reflects the vasomotor diameter variations at a frequency of approximately 0.1 Hz. Therefore, vasomotion must be considered when judging NC purely based on diameter measurements.

Dynamic Vessel Analyzer measurement of a vein with a mean diameter of 157.1 μm: (a) typical (normalized) diameter variations as recorded by DVA over 10 minutes. Sliding averages were calculated for a sliding window of 3 seconds (red, consistent with the Doppler OCT recording time) and 20 seconds (green, consistent with the minimum DVA averaging time used in this study). (b) Shows the same DVA recording and the sliding averages but only for an interval of 50 seconds. (c) Fast Fourier transform of the vessel diameter. Two pronounced peaks are visible, one corresponding to the frequency of the heart beat (∼0.73 Hz) and one that reflects the vasomotor diameter variations at a frequency of approximately 0.1 Hz.

Figure A1

Dynamic Vessel Analyzer measurement of a vein with a mean diameter of 157.1 μm: (a) typical (normalized) diameter variations as recorded by DVA over 10 minutes. Sliding averages were calculated for a sliding window of 3 seconds (red, consistent with the Doppler OCT recording time) and 20 seconds (green, consistent with the minimum DVA averaging time used in this study). (b) Shows the same DVA recording and the sliding averages but only for an interval of 50 seconds. (c) Fast Fourier transform of the vessel diameter. Two pronounced peaks are visible, one corresponding to the frequency of the heart beat (∼0.73 Hz) and one that reflects the vasomotor diameter variations at a frequency of approximately 0.1 Hz.

Model of the retinal vasculature represented by a binary tree. The vessels bifurcate in a dichotomous manner except for the precapillaries, which are point of origin of four capillaries. Adapted from Takahashi et al.33

Figure 3

Model of the retinal vasculature represented by a binary tree. The vessels bifurcate in a dichotomous manner except for the precapillaries, which are point of origin of four capillaries. Adapted from Takahashi et al.33

Relative diameter changes applied in the binary tree model to simulate different flow states. For scenario 1, the increase in diameter decreases from 20% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (red). In scenario 2, the increase in diameter accumulated from 0% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (blue). In scenario 3, the increase in diameter accumulated from 8% in the largest artery to 9.8% in the largest vein (green). The x-axis of the plot corresponds to the layer of the vascular tree.

Figure 4

Relative diameter changes applied in the binary tree model to simulate different flow states. For scenario 1, the increase in diameter decreases from 20% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (red). In scenario 2, the increase in diameter accumulated from 0% in the layer containing the smallest vessels to 8% in the largest artery and 9.8% in the largest vein (blue). In scenario 3, the increase in diameter accumulated from 8% in the largest artery to 9.8% in the largest vein (green). The x-axis of the plot corresponds to the layer of the vascular tree.

Total arterial blood flow and TVBF over CRAE and CRVE, respectively, at baseline and during flicker stimulation. Central retinal arterial equivalent and TABF correlated well in the subjects at baseline (black) and during flicker stimulation (blue). Central retinal venous equivalent and TVBF correlated well at baseline (red), but weak during the flicker stimulation (pink).

Figure 7

Total arterial blood flow and TVBF over CRAE and CRVE, respectively, at baseline and during flicker stimulation. Central retinal arterial equivalent and TABF correlated well in the subjects at baseline (black) and during flicker stimulation (blue). Central retinal venous equivalent and TVBF correlated well at baseline (red), but weak during the flicker stimulation (pink).

Flow over diameter in a log-log plot for individual vessels in the four simulated flow states (baseline + three vasodilation scenarios during flicker stimulation) for arteries (a) and veins (b). The respective exponent of the power fit to the data series of each scenario is given in the legends of (a) and (b).

Figure 10

Flow over diameter in a log-log plot for individual vessels in the four simulated flow states (baseline + three vasodilation scenarios during flicker stimulation) for arteries (a) and veins (b). The respective exponent of the power fit to the data series of each scenario is given in the legends of (a) and (b).

(a) Absolute pressure for the simulated vessel segments (mean of the pressures at the inflow and outflow point of each segment) plotted over the corresponding vessel diameters for baseline and all three scenarios. (b) Relative changes of the pressure gradients compared with the baseline system for each layer.

Figure 11

(a) Absolute pressure for the simulated vessel segments (mean of the pressures at the inflow and outflow point of each segment) plotted over the corresponding vessel diameters for baseline and all three scenarios. (b) Relative changes of the pressure gradients compared with the baseline system for each layer.

Dynamic Vessel Analyzer measurement of a vein with a mean diameter of 157.1 μm: (a) typical (normalized) diameter variations as recorded by DVA over 10 minutes. Sliding averages were calculated for a sliding window of 3 seconds (red, consistent with the Doppler OCT recording time) and 20 seconds (green, consistent with the minimum DVA averaging time used in this study). (b) Shows the same DVA recording and the sliding averages but only for an interval of 50 seconds. (c) Fast Fourier transform of the vessel diameter. Two pronounced peaks are visible, one corresponding to the frequency of the heart beat (∼0.73 Hz) and one that reflects the vasomotor diameter variations at a frequency of approximately 0.1 Hz.

Figure A1

Dynamic Vessel Analyzer measurement of a vein with a mean diameter of 157.1 μm: (a) typical (normalized) diameter variations as recorded by DVA over 10 minutes. Sliding averages were calculated for a sliding window of 3 seconds (red, consistent with the Doppler OCT recording time) and 20 seconds (green, consistent with the minimum DVA averaging time used in this study). (b) Shows the same DVA recording and the sliding averages but only for an interval of 50 seconds. (c) Fast Fourier transform of the vessel diameter. Two pronounced peaks are visible, one corresponding to the frequency of the heart beat (∼0.73 Hz) and one that reflects the vasomotor diameter variations at a frequency of approximately 0.1 Hz.